arXiv Open Access 2026

Is it true that no mathematical relation exists between the Navier-Stokes equations and the multifractal model?

John D. Gibbon Dario Vincenzi
Lihat Sumber

Abstrak

Contrary to accepted turbulence folklore, which holds that no mathematical relation exists between the Navier-Stokes equations (NSEs) and the multifractal model (MFM) of Parisi and Frisch, we develop a theory that reconciles the MFM with Leray's weak solutions of Navier-Stokes analysis. From a combination of Euler invariant scaling and the NSEs we also derive the Paladin-Vulpiani inverse scale $Lη_{h,pav}^{-1} = Re^{1/(1+h)}$ which acts as a mediator between the two theories. This is achieved by considering $L^{2m}$-norms of the velocity gradient to find a correspondence between $m$ and the local scaling exponent $h$ in the multifractal model. The parameter $m$ acts as if it were the sliding focus control on a telescope which allows us to zoom in and out on different structures. The range $1 \leqslant m \leqslant \infty$ is equivalent to $-2/3 \leqslant h_{min} \leqslant 1/3$, which lies precisely in the region where Bandak et al. (2022, 2024) have suggested that thermal noise makes the NSEs inadequate and generates spontaneous stochasticity. The implications of this are discussed.

Topik & Kata Kunci

Penulis (2)

J

John D. Gibbon

D

Dario Vincenzi

Format Sitasi

Gibbon, J.D., Vincenzi, D. (2026). Is it true that no mathematical relation exists between the Navier-Stokes equations and the multifractal model?. https://arxiv.org/abs/2603.19125

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Tahun Terbit
2026
Bahasa
en
Sumber Database
arXiv
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Open Access ✓